[tuning-math] Re: Transformations of glumma

I checked each of these 12 scales for intervals which were close to a
7-limit consonance by a comma less than 15 cents. All of them had at
least one such comma, and the 31-et covers all of the commas.


> reca1b2 := [1, 21/20, 35/32, 6/5, 5/4, 21/16, 35/24, 3/2, 49/32, 
> 12/7,
> 7/4, 
> 9/5];

126/125 ^ 1728/1715 = [10, 9, 7, -9, 17, -9]

"Small diesic" temperament covered by 27, 31 and 58

> reca1b3 := [1, 15/14, 35/32, 6/5, 5/4, 9/7, 35/24, 3/2, 25/16, 12/7, 
> 7/4,
> 15
> /8];

1728/1715

> reca2b1 := [1, 25/24, 21/20, 35/32, 5/4, 21/16, 10/7, 35/24, 3/2, 
> 49/32,
> 5/3
> , 7/4];

126/125

> reca2b3 := [1, 21/20, 15/14, 9/8, 5/4, 21/16, 10/7, 3/2, 5/3, 7/4, 
> 25/14,
> 15
> /8];

126/125

> reca3b1 := [1, 49/48, 15/14, 35/32, 7/6, 5/4, 7/5, 35/24, 3/2, 25/16,
> 7/4, 
> 15/8];

225/224

> reca3b2 := [1, 21/20, 15/14, 9/8, 7/6, 49/40, 5/4, 21/16, 7/5, 3/2, 
> 7/4,
> 15/
> 8];

126/125 ^ 225/224 ^ 2401/2400 = 31-et

> reca1c2 := [1, 25/24, 35/32, 8/7, 6/5, 5/4, 10/7, 35/24, 3/2, 5/3, 
> 12/7,
> 7/4
> ];

126/125 ^ 1728/1715, small diesic

> reca1c3 := [1, 49/48, 35/32, 7/6, 6/5, 5/4, 7/5, 35/24, 3/2, 8/5, 
> 12/7,
> 7/4]
> ;

1728/1715

> reca2c1 := [1, 21/20, 8/7, 6/5, 5/4, 21/16, 10/7, 3/2, 5/3, 12/7, 
> 7/4,
> 9/5];

1029/1024^126/125 = [9, 5, -3, -21, 30, -13]

"quartaminorthirds" covered by 31, 46 and 77

> reca2c3 := [1, 21/20, 7/6, 49/40, 5/4, 21/16, 4/3, 7/5, 10/7, 3/2, 
> 5/3,
> 7/4]
> ;

2401/2400^126/125 = 126/125^1728/1715 = small diesic

> reca3c1 := [1, 15/14, 7/6, 6/5, 5/4, 9/7, 7/5, 3/2, 8/5, 12/7, 7/4,
> 15/8];

225/224

> reca3c2 := [1, 15/14, 7/6, 5/4, 4/3, 7/5, 10/7, 3/2, 5/3, 7/4, 25/14,
> 15/8];

126/125^225/224 = [1, 4, 10, 12 -13, 4]

meantone, covered by 19, 31, 43, 50, 74

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